687320550
Name_ _____________________
Exam 2
Thursday, 17 April 2008
Page 1 of 22
******BE SURE TO SCROLL ALL THE WAY TO END!!!




Formula sheet will be provided … see below…
Bring ruler with millimeter markings
Bring a protractor (unlikely, but just in case)
Bring a fully charged calculator
Descriptions of some of the topics covered

Unit conversion (Conversion relations will be given)

Scientific notation

Significant figures and rules for arithmetic operations

Measurement uncertainty

Proper form

Two dimensional motion problems similar to the examples covered
in class.

Newton’s Second Law problems
2/6/2016
687320550


Name_ _____________________
Page 2 of 22
******BE SURE TO SCROLL ALL THE WAY TO END!!!
Formula sheet (preliminary)
---------------------------------------------------------------------------------------------------------------
Significant figures:





In Dr. Entenberg’s class, trailing zeroes will be meaningful unless the number has quotes around it, i.e. “75,000” nails.
Use a decimal point when you know the correct number of significant figures.
Whole numbers have no decimal point; e.g., 3 = 3.0000000…….
If unsure, use scientific notation to determine the number of significant figures.
Proper form: (A + A) where A must be written to 1 significant figure
Note that A and A must have
1. Common exponent outside the parentheses
2. Common units outside the parentheses
3. Same number of decimal places (inside the parentheses)
Scientific notation example: 3769. m = 3.769 X 103 m
Uncertainty propagation examples:

f=X*Y
f = fmax – f where fmax = (X + X) * (Y + Y)

f=X/Y
f = fmax – f where fmax = (X + X) / (Y – Y)
---------------------------------------------------------------------------------------------------------------Constants
g = 9.80 m/s2 g = 980. cm/s2 g = 32.2 ft/s2
Geometry
2R
Trigonometry
sine = opposite/hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite/adjacent = sine/cosine
 R2
4  R2
(4/3)  R3
 R2 H
---------------------------------------------------------------------------------------------------------------Vectors in 2-D
Symbol
Vectors in 2-D
F = |F| = magnitude ( + ONLY)
 = angle wrt a given direction ( + )
Vectors in 2-D
Fx = component along x direction ( + ) Fy = component along y direction ( + )
Fx= + F cos  (or Fx= + F sin ’)
Fy= + F sin  (or Fy= + F cos ’)
Force and Vector NOTATION:
2/6/2016
687320550
Name_ _____________________

    
Fnet   F  F1  F2  F3  F4   =
Page 3 of 22
Fnet =  F = F1 + F2 + F3 + F4….
Variables, definitions, and equations
Mass
m or M
___________________________________Equations of motion
Position
X
Displacement
X = Xfinal – Xinitial
Average velocity
(Vx)avg = X / t
Average acceleration
(aX)avg = Vx / t
Equations of motion
Y
Y = Yfinal – Yinitial

(VY)avg = Y / t
(aY)avg = VY / t
Constant acceleration equations
Velocity time equation
Position time equation
Velocity position equation
aX = (aX)avg = constant
Vxf = Vxi + ax t
Xf = Xi + Vxi t + ½ ax t2
Vxf 2 = Vxi 2 + 2 ax X
aY = (aY)avg = constant
VYf = VYi + aY t
Yf = Yi + VYi t + ½ aY t2
VYf 2 = VYi 2 + 2 aY Y
Force: Newton’s Second Law
 Fx = M ax
 FY = M aY
Various Force Magnitudes
Weight magnitude
Friction force magnitude
Normal force magnitude
Tension force magnitude

2/6/2016
Wt = M g
fs < fsmax fsmax =s Fn
fkin = k
Fn or n
Ft or T
687320550
Name_ _____________________
Page 4 of 22
Example 3.11 Planning a Hollywood stunt Suppose a stunt man drives a car off
a 10.0 m high cliff at a speed of 20.0 m/s. How far does the car land from the base
of the cliff? Answer: 29.0 m.
Procedure: Diagram, specify known information, write EOMs, find unknowns.
2/6/2016
687320550
Name_ _____________________
Page 5 of 22

At t = 0, you stand at the origin and throw a football at an angle 35.0  with
respect to the +x-axis. The ball reaches a maximum height (Point B) in its trajectory
and then comes back to the same level it started at. The ball leaves your hand with
a speed of 70.0 m/s.
A
B
C
V0
Y axis
V0
35.0 
X axis
(a) On diagram above, sketch and label the velocity vector and acceleration vector of the football at each of the points where the
dashed lines A, B, and C intersect with the trajectory.
(c) How long does it take the football to reach the top of its trajectory (Point B)?
(d) How far does the football go before it comes back to the X axis?
2/6/2016
687320550
Name_ _____________________
Page 6 of 22

Example DONE IN CLASS Projectile (say a ball) is launched at a speed of 22.0 m/s and at an angle
of 63.0° to the horizontal. See Figure 3.30 a and b below.
(a)
(b)
(c)
(d)
(e)
Write down the independent X and Y “equations of motion” for this situation.
How long does it take the ball to reach the top of its trajectory?
What is the maximum height of the ball?
How long (time of flight) is the ball in the air?
How far does the ball go? (What is its range?)
A SIMILAR PROBLEM WITH ANSWERS

At t = 0 , you stand at the origin and throw a ball at an angle of 30.0 degrees (Counter-Clockwise) with respect to the positive x-axis. The
ball leaves your hand with a speed of 65.0 m/s. The ball reaches a maximum height in its trajectory and then is caught by someone at the same
height at which it was thrown.
(a) Start by drawing a picture of the ball’s parabolic trajectory. Let the ball start at the origin of an x-y coordinate system. Sketch and label the
vectors for velocity, and acceleration when the ball has moved about 25%, 50%, 75%, and 100% of its total path.
(b) On your picture, sketch and label the following: Vo, Vox, Voy ; indicate the x and y directions. Calculate the components Vox and Voy of
the initial velocity at time t = 0. (56.3 m/s, 32.5 m/s)
(c) Write down the “general” and “specific” position and velocity equations of motion for both the x motion and the y motion.
(d) Calculate the time that it takes the ball to rise to its greatest height. Hint: Remember, x and y motions are completely independent. What is
true about Vy at this time ? (3.32 s)
(e) Calculate the “range” of the ball. Do not use range formula. (374. m)
(f) Calculate the “maximum height” of the ball. (54.0 m)
(g) Calculate the velocity components of the ball at the instant before it is caught. (56.3 m/s, -32.5 m/s)
2/6/2016
687320550

Name_ _____________________
Page 7 of 22
A 70.0 kg crate is at rest on a horizontal surface. A man pulls to the LEFT on a crate with a
rope. The rope is along the horizontal direction. The tension in the rope is 450. N. As
the crate slides along the floor, its motion is opposed by a kinetic friction force of magnitude
140. N.
y axis
Ft
x axis
(a) On the free body diagram to the right,
sketch and label all forces acting ONLY
on the crate. Sketch the tail of each force at
the approximate location where the force acts.
(b) Calculate the x component of the acceleration vector for the crate.
(c) What is the x component of velocity after 10 seconds for the crate?
(d) What is the y component of acceleration vector for the crate? Explain.
2/6/2016
687320550
Name_ _____________________
IN CLASS PROBLEM
Page 8 of 22
Example 5.2 “Readying a wrecking ball”
(a) RECOPY THE FBD. Work with force magnitudes. T1, T2, W = M g
What is a
magnitude?

Identify the unknown magnitudes.
(b) Use trigonometry to write the X and Y components of each of the three forces. Get your
answers to 3 significant figures.
(c) Use Newton’s 2nd Law (for static equilibrium) to generate 2 equations in 2 unknowns.
The 2 unknowns are T1 and T2.
(d) Solve the equations for part (c).
2/6/2016
687320550
Name_ _____________________
Page 9 of 22
IN CLASS PROBLEM
Example 5.3 Tension in towing a car at a constant velocity
(zero acceleration or “dynamic equilibrium”) Note: Fnet = 0 even though the car is in
moving!!
(a) What is a magnitude?

Re-sketch the free body diagram using only force “magnitudes and angles.”
(b) Use trigonometry to write the X and Y components of each of the four forces. Get your
answers to 3 significant figures. What is the difference between a magnitude and a
component?
(c) Make a motion diagram for the car.
(d) Use Newton’s 2nd Law to generate 2 equations in 2 unknowns. The 2 unknowns are N
and T. Solve the equations for the unknowns.
2/6/2016
687320550
Name_ _____________________
Page 10 of 22
IN CLASS PROBLEM
Example 5.5 Tension in towing a car with constant acceleration (not in equilibrium!)
(a) What is a magnitude? Re-sketch the free body diagram using only force “magnitudes
and angles.”
(b) Use trigonometry to write the X and Y components of each of the four forces. Get your
answers to 3 significant figures. What is the difference between a magnitude and a
component?
(c) Make a motion diagram for the car.
(d) Use Newton’s 2nd Law to generate 2 equations in 2 unknowns. The 2 unknowns are N
and T. Solve the equations for the unknowns.
2/6/2016
687320550
Name_ _____________________
Page 11 of 22
 Example 5.15 Pushing two blocks. (VARIATION)
Figure 5.33 shows a 5.00 kg block A being pushed
with a 3.00 N force. In front of this block is a 10.0
kg block B; the two blocks move together. (Do all
calculations to 3 sig figs.)
(a)
Make an FBD of the combined system.
Use N-2 to obtain the acceleration of the combined
system.
(b) Make an FBD for just block A. Use N-2 to find the force magnitude Fon A by B on block A
by block B?
(c) Make an FBD for just block B. Use N-2 to find the force magnitude Fon B by A on block B
by block A?
2/6/2016
687320550
Name_ _____________________
IN CLASS PROBLEM
Page 12 of 22
Answer M2 = 34.1 kg
 Given two masses M1 and M2 of unknown mass. The tension in the rope
between the masses is 450 N and the magnitude of the applied force is 875 N.
There is a 160 N kinetic friction force operating on M2. The acceleration of both
masses is to the right at 7.77 m/s2.
Fa
Ftension
M1
M2
a
X axis
(a)
Sketch and label the forces on only M2 by using
the box to the right to make a free-body diagram.
(b)
Starting with Newton’s Second Law, Fnet =  Fx = M ax,
determine the mass of M2.
2/6/2016
M2
687320550

Name_ _____________________
Page 13 of 22
Show that the gravitational acceleration 9.800 m/s2 is equivalent to 32.15 ft/s2 .

Give the name of the SI force unit and express it in terms of the three
fundamental SI units.

Calculate the "weight" and "mass" for each of the following. Give your
answer in both BE and SI units. [HRF3,5-15E]
(a) a 5.00 pound bag of sugar.
(b) a 240. lb fullback.
(c) a 1.80 ton automobile.

A man “weighs” 800. N.
(a) Determine his weight and mass in SI units.
(b) Determine his weight and mass in BE units.
(c) Determine his weight and mass in CGS units.
2/6/2016
687320550
Name_ _____________________
Page 14 of 22

You are walking on the floor in the positive X direction. Study the following
figure (4.35 a from MP) and then answer the questions.
(d) Make a diagram which shows all forces on
your body, the floor, and the earth as you are
walking.
(e) Make a FBD of your body as it is walking.
(f)
What is the origin of the force which causes you to move forward?
2/6/2016
687320550
Name_ _____________________
Page 15 of 22

A plane moves with a constant velocity in a straight line. The plane moves a distance
of (955. + 6.) meters over a time of (3.13 + 0.07) seconds.
(a) Calculate the speed V of the plane. Give a preliminary answer to 5 significant figures and in scientific notation.
(b) Calculate V, the absolute uncertainty of V. Give a preliminary answer to 3 significant figures.
(c) Write V to one significant figure.

Use V to determine the correct number of significant figures for V.

Write V with the correct number of significant figures and in “proper form.”
2/6/2016
687320550
Name_ _____________________
Page 16 of 22
 A box of books is initially at rest on a floor. The mass of the box is 90.0 kg. The coefficients of static and kinetic
friction for the bottom of the box and the floor are µs = 0.700 and µk = 0.600 . Let the applied force Fapp on the box
be horizontal in the positive X direction.
Y
direction
X
direction
(a) On the above figure, sketch and label the forces (which only act) on the box.
(b) Calculate the magnitude of the normal force.
(c) For the following table, calculate the magnitude of the friction force and state whether the box is moving or not.
Fapplied
Does box move ? If so, what is the acceleration aX?
Show work on back if more space is required.
___________________________________________________________________________________
0N
___________________________________________________________________________________
50 N
___________________________________________________________________________________
100 N
___________________________________________________________________________________
250 N
___________________________________________________________________________________
400 N
___________________________________________________________________________________
600 N
___________________________________________________________________________________
650 N
___________________________________________________________________________________
700 N
___________________________________________________________________________________
2/6/2016
Friction Force
687320550
Name_ _____________________
Page 17 of 22
Y axis
Fapp
X axis

A 60.0 kg box of books is initially at rest on the floor. At t = 0, you start to pull on the box in the x direction. The
coefficient of static friction is 0.750 and the coefficient of kinetic friction is 0.650. A horizontal force Fapp is applied to the box in the
positive x-direction.
Suggestion: Start by showing all forces that act only on the box in the above diagram.
_______ When the horizontal applied force is 140. N, the friction force magnitude will be
(a) 0 N
(b) 140. N
(c) 382. N
(d) 441. N
(e) 588. N
_______ When the horizontal applied force is 330. N, the friction force magnitude will be
(a) 0 N
(b) 330. N
(c) 382. N
(d) 441. N
(e) 588. N
_______ When the horizontal applied force is 520. N, the friction force magnitude will be
(a) 0 N
(b) 520. N
(c) 382. N
(d) 441. N
(e) 588. N
_______ When the horizontal applied force is 520. N, the horizontal acceleration will be
(a) 0 N
(b) 1.32 m/s2
(c) 2.30 m/s2
(d) 8.67 m/s2
(e) 9.80 m/s2
_______ When you walk on a sidewalk, force that enables you to move forward without sliding is
(a) the kinetic friction force on the ground by your shoe
(b) the kinetic friction force on your shoe by the ground
(c) the static friction force on the ground by your shoe
(d) the static friction force on your shoe by the ground
_______ You twirl a ball on a string in a circle. Ignoring the effect of gravity, the force that causes the ball to move in a circle is
(a) the tension force on the ball by the string
(b) the tension force on the string by the ball
(c) the tension force on the string by your hand
(d) the tension force on your hand by the string
_______ You run (without sliding) in a circle around a track. The force that causes you to move in a circle is
2/6/2016
687320550
Name_ _____________________
(a) the force of kinetic friction on your shoe by the track surface
(b) the force of kinetic friction on the track surface by your shoe
(c) the force of static friction on your shoe by the track surface
(d) the force of static friction on the track surface by your shoe
Page 18 of 22
_______ You run (without sliding) in a circle around a track. The reason you must lean inward towards the center of the circle is to
(a) push inward on the track so that the track pushes outward on you
(b) push outward on the track so that the track pushes inward on you
(c) decrease your normal force to facilitate circular motion
(d) decrease your apparent weight to facilitate circular motion
2/6/2016
687320550
Name_ _____________________
Page 19 of 22

A man uses a pole to push a 85.0 kg crate across a rough horizontal surface. The pole makes an angle of 39.0 with respect
to the horizontal direction. The magnitude of the “applied” pushing force on the crate by the pole is 350 N. As the crate accelerates
along the floor, its motion is opposed by a kinetic friction force of magnitude 130 N.
Fapp
y axis
39.0
x
axis
(a) Draw a free body diagram for the crate below.
 Sketch and label all force magnitudes acting only on the crate. Show components on forces not completely
horizontal or completely vertical.
 Illustrate all pertinent angles on your diagram.
(b) Starting with Newton’s 2nd Law, obtain the horizontal acceleration of the crate.
(c) Starting with Newton’s 2nd Law, obtain the magnitude of the normal force acting on the crate.
(d) At t = 0, the crate has a speed of 2.00 m/s. How far does the crate move in 5.00 s?
2/6/2016
687320550
Name_ _____________________
Page 20 of 22
NOTE: THE FOLLOWING ARE PRACTICE PROBLEMS ONLY. SOME OF THEM HAVE NUMERICAL ANSWERS. YOU ARE
NOT RESPONSIBLE FOR THEM UNLESS THEY HAVE BEEN DONE IN CLASS!!

“RIFLE PROBLEM” At t = 0, a rifle is fired horizontally at a target which is at the same level as the rifle; the target, mounted on a wall, is
30.5 m from the end of the rifle. The bullet strikes the wall at a distance of 7.62 cm below the center of the target.
(a) Make a sketch of the rifle, the target, and the trajectory of the bullet. Let the origin of an x-y coordinate system be at the end of the rifle. At
the middle of the trajectory, sketch and label the position vector (and its components), the velocity vector (and its components), and the
acceleration vector (and its components).
(b) How long does it take the bullet to reach the wall? (0.125 s)
(c) What are the x and y velocity components of the bullet when it leaves the gun? (244. m/s, 0 m/s)
(d) What are the velocity components of the bullet the instant before it strikes the wall? (244. m/s, -1.23 m/s)

A dockworker loading crates on a ship finds that a 20 kg crate, initially at rest on a rough horizontal surface, requires a 75 N
horizontal force to set it in motion. However, after it is in motion, horizontal force of 60 N is required to keep the crate moving with a
constant speed. Find the coefficients of static and kinetic friction between the crate and the floor. (.383,.306)

To move a box of books along the floor, it is necessary for a rope to have a tension of 80.0 N at an angle of 35.0 degrees.
The box of books has a mass of 25.0 kg and the coefficient of kinetic friction between the box and the floor is 0.300.
(a) Make a free-body diagram of all the forces acting on the box. On your diagram, illustrate the x and y components of the tension
force of the rope on the box; also, calculate these components.
(b) Calculate the normal force on the box.
(c) Calculate the magnitude of the kinetic force of friction on the box.
(d) Use Newton's second law to calculate the horizontal acceleration of the box.
[SF2, Example 3.5] (65.5 N,45.9 N,199 N,59.7 N,0.232 m/s2)

A man is applying a horizontal force to drag a 200. kg box of books on a floor whose static and kinetic coefficients of friction
are 0.500 and 0.450. The box is moving with a constant speed of 2 m/s. Calculate the magnitude of the force that the man applies
to the box. (882. N)
2/6/2016
687320550
Name_ _____________________
Page 21 of 22
NOTE: THE FOLLOWING ARE PRACTICE PROBLEMS ONLY. SOME OF THEM HAVE NUMERICAL ANSWERS. YOU ARE
NOT RESPONSIBLE FOR THEM UNLESS THEY HAVE BEEN DONE IN CLASS!!
 A 160. pound man stands on a bathroom scale in an elevator which has the following velocity time graph.
Useful information: g = 32.0 ft / s2
VY (m/s)
10 m/s
t (s)
0
1
2
3
4
5
(a) Make a free body diagram of the man in the elevator.
6
7
8
Scale
(b) What does the scale read between times 0 and 2 s? (Hint: calculate the acceleration and use Newton’s 2nd Law as we did in
class.)
(c) What does the scale read between times 2s and 5 s?
(d) What does the scale read between times 5 s and 7 s?
2/6/2016
687320550
Name_ _____________________
Page 22 of 22
NOTE: THE FOLLOWING ARE PRACTICE PROBLEMS ONLY. SOME OF THEM HAVE NUMERICAL ANSWERS. YOU ARE
NOT RESPONSIBLE FOR THEM UNLESS THEY HAVE BEEN DONE IN CLASS!!

A hockey stick is used to apply a constant force of 3.75 N to a hockey puck in the positive x-direction. There is a kinetic
friction force of 1.25 N of the puck by the surface of the ice. The puck, which is initially at rest at the origin, has an acceleration of
20.0 m/s2.
(a) Make a sketch of the puck on the ice. Sketch and label only the forces on the puck.
(b) Starting with the expression for Newton’s Second Law, determine the mass of the hockey puck.
(c) What is the weight of the puck in CGS units?
(d) At what time will the puck have a speed of 9.85 m/s?
_______ A satellite, mass M, has a circular orbit about the Earth, mass ME and radius RE. The height of the satellite is H above sea
level. The force that causes the satellite to move in a circle is
(a) M g
(b) M G ME / RE2
(c) M G ME / (RE + H)2
(d) M g ME / (RE + H)2
_______ The true weight of an object, mass M, at rest on the Moon, mass MM and radius RM, is
(a) M g
(b) M G ME / RE2
(c) M G MM / RM2
(d) M g MM / RM2

On the diagram, the Moon (black dot) moves clockwise in uniform circular motion around the Earth. The average (center to
center) distance of the Moon from the Earth is 3.85 x 108 meters. The mass of the Earth is 5.98 x 1024 kg and the mass of the
Moon is 7.35 x 1022 kg.
(a) Use the black dot to the right to make a free body diagram of the moon at the same instant it is shown in the diagram. Label all
forces on the Moon.
(b) On the diagram, sketch and label the acceleration of the Moon.
(c) On the diagram, sketch and label the tangential velocity of the Moon.
(d) Calculate the centripetal force on the Moon.
2/6/2016